To apply the visualization tools described above to sparse functional data, we required an appropriate data fitting and depth for data ordering. On the basis of MFPCA ([1]} [1]}), we improved the fitting of data through the iterated expectation from bootstrap ([3]} [3]}). We took the multivariate functional halfspace depth (MFHD, [5]} [5]}) as a building block for proposing various revised depths for sparse multivariate functional data. We obtained the best depth via the Spearman rank coefficient simulated in various data settings and sparseness scenarios. In the univariate functional setting, MFPCA became UFPCA ([7]} [7]}), and we used the modified band depth (MBD, [9]} [9]}) to order the data before applying the functional tools.
